Category Archives: Statistics

Conflict and Confidence: MBH99

Here’s a first attempt at applying the techniques of Brown and Sundberg 1987 to MBH99. The results shown here are very experimental, as I’m learning the techniques, but the results appear very intriguing and to hold some possibility for linking temperature reconstructions to known statistical methodologies – something that seems more scientifically useful than “PR […]

Brown and Sundberg: "Confidence and conflict in multivariate calibration" #1

Introduction If one is to advance in the statistical analysis of temperature reconstructions, let alone climate reconstructions – and let’s take improving the quality of the data as the obvious priority – Task One in my opinion is to place the ad hoc Team procedures used in reconstructions in a statistical framework known off the […]

Calibration in the Mann et al 2007 Network Revisited

In a post a few months ago, I discussed MBH99 proxies (and similar points will doubtless apply to the other overlapping series) from the point of view of the elementary calibration diagram of Draper and Smith 1981 (page 49), an older version of a standard text. Nothing exotic. One of the problems that arose in […]

Koutsoyiannis 2008 Presentation

Anything by Demetris Koutsoyiannis is always worth spending time on. Spence_UK draws our attention to this recent presentation at AGU asking: How well do the models capture the scaling behaviour of the real climate, by assessing standard deviation at different scales. (Albeit at a regional, rather than global level). Assessment of the reliability of climate […]

Squared Weights in MBH98

A couple of weeks ago, I said that I would document (at least for Jean S and UC) an observation about the use of squared weights in MBH98. I realize that most readers won’t be fascinated with this particular exposition, but indulge us a little since this sort of entry is actually a very useful […]

PC Weights on a Square Region

A few days ago, I showed some plots showing distribution of weights arising from principal components carried out on data from a region arranged as a line segment (think Chile). Today I’ve done a similar analysis for a square shaped region again assuming spatial autocorrelation governed by distance. In this case, I made a regular […]

PCs in a Linear Network with Homogeneous Spatial Autocorrelation

As I observed a couple of posts ago, the Stahle SWM network can be arranged so that its correlation matrix is closely approximated by a Toeplitz matrix i.e. there is a “natural” linear order. I also noted that results from matrix algebra proving that, under relevant conditions, all the coefficients in the PC1 were of […]

More on Toeplitz Matrices and Tree Ring Networks

Yesterday’s results connecting eigenvector patterns in the Stahle SWM network to Toeplitz matrices and spatial autocorrelation were obviously pretty interesting. Needless to say, I was interested to test these ideas on out some other networks and see how they held up. There is a large literature on spatial autocorrelation and there appear to be well-known […]

Toeplitz Matrices and the Stahle Tree Ring Network

One of the most ridiculous aspects and most misleading aspects of MBH (and efforts to rehabilitate it) is the assumption that principal components applied to geographically heterogeneous networks necessarily yield time series of climatic interest. Preisendorfer (and others) state explicitly that principal components should be used as an exploratory method – and disavowed any notion […]

Data Smoothing and Spurious Correlation

Allan Macrae has posted an interesting study at ICECAP. In the study he argues that the changes in temperature (tropospheric and surface) precede the changes in atmospheric CO2 by nine months. Thus, he says, CO2 cannot be the source of the changes in temperature, because it follows those changes. Being a curious and generally disbelieving […]